Consistent histories is where I put my money- the homogenous history class operator seems potentially like the missing piece.
Hmm, I could never make sense of the formalism of CH (it seems to rely on time-ordering and density matrices, neither of which inspire confidence, given that one expects a relativistically invariant evolution of a pure state), and the popular write-ups sound like advocacy.
Why would you expect relativistic invariance? The Schroedinger equation isn’t even Galilean invariant ( the mass comes through as a central charge, the probabilities are Galilean but not lorentz invariant)
The best reference for consistent histories is Bob Griffith’s excellent text (not to be confused with the other Griffiths)
Because I would expect a model that has a hope in hell of getting deeper toward the measurement problem than “shut up and calculate” to give a relativistically invariant account of the EPR, and because I expect such a model to be built on top of some form of QFT (as I mentioned in another reply, the number of particles is not conserved during the measurement, so the Hilbert space doesn’t cut it, you need something like a Fock space, second quantization etc.).
But the only way you are going to get relativistic invariance is to throw out the Schroedinger equation. The hope is that an interpretation makes it easier to move to QFT, NOT that a given interpretation will be Lorentz invariant (which is impossible, given the Schreodinger equation).
So far none of the interpretations of quantum are built on top of QFT, mostly because QFT isn’t yet formalized, its a hodge podge of heuristics that gets the right answer. The handful of axiomatic field theories don’t actually describe physical systems. Some people have a pipe dream that finding better quantum axioms will point the way toward better QFT axioms, but I’m not in that camp.
The SE should be a non-relativistic limit of whatever model is the next step. Not sure if it requires a formalization of QFT, it just needs to make decent predictions. Physicists are not overly picky. As long as it’s reasonably self-consistent. Or not even. As long as it helps you calculate something new and interesting unambiguously.
QFT IS the obvious next-step, but the reason people play with standard quantum formulations instead of trying to work in the context of QFT and ‘push the interpretation down’ is that QFT isn’t yet on firm footing.
Hmmm… apparently making QM play nice with Special Relativity isn’t quite as simple as using the Dirac equation instead of the Schrodinger equation, because the Dirac equation has negative energy solutions, and making it impossible for electrons to “decay” into these negative energy states requires kludges.
Quantized wave function solves the negative energy problem, at the expense of introducing a bunch of infinities, some of which are easier to work around (renormalize) than others. For example, there is no way to usefully quantize gravitational field.
This isn’t quite true. What solves the problem isn’t quantizing wave functions, its insisting that positive energy propagate forward in time- i.e. picking the Feynman propagator (instead of the retarded or advanced propagator, etc) that solves the problem. You still have to make a division between the positive energy and negative energy pole in the propagator (unfortunately, all observers can’t agree on which states have positive and what states have negative energy, which is the basis of the Unruh effect- two observers accelerating relative two each other cannot agree on particle number).
Also, its a misconception that you can’t simply quantize the gravitational field. If you treat GR as an effective theory you can make calculations of arbitrary accuracy with a finite number of measured parameters, with just canonical quantization. The standard model is ALSO not a renormalizable field theory (not since the addition of neutrino masses). Weinberg has recently tried to make the argument that maybe GR + canonical quantization (i.e. gravity is asymptotically safe)
Thanks for the corrections, my area is mostly classical GR, not Standard Model physics. And a good point on the Unruh effect. As for quantizing GR, note the “useful” disclaimer. I am deeply suspicious of any technique that treats GR as an effective field theory on some background spacetime, as it throws away the whole reason why GR is unlike any other field theory. Weinberg is especially prone to to doing that, so, while I respect anything he does in HEP, I don’t put much stock into his GR-related efforts. If anything, I expect the progress to come from the entropic gravity crowd, with nothing to quantize.
When I worked in physics I did perturbative QCD stuff in graduate school and then effective theories for medium energy scattering, and finally axiomatic quantum field theories as a postdoc before I left physics for a field with actual employment opportunities (statistics/big data stuff).
But why shouldn’t GR be treated as just another field theory? It certainly has the structure of a field theory. Feynman and then Weinberg managed to show that GR is THE self-consistent, massless spin-2 field theory- so to that extent it IS just another field theory.
Treating GR as an effective theory works. I doubt that the theory is asymptotically safe, but for an effective theory, who cares? Why should we treat the matter part of the action any differently than we treat the spacetime piece of the action?
But why shouldn’t GR be treated as just another field theory? It certainly has the structure of a field theory.
That’s a separate discussion, but let me just note that the action would have to be summed not just over all paths (in which spacetime?), but also over all possible (and maybe impossible) topologies, as well.
Hmm, I could never make sense of the formalism of CH (it seems to rely on time-ordering and density matrices, neither of which inspire confidence, given that one expects a relativistically invariant evolution of a pure state), and the popular write-ups sound like advocacy.
Why would you expect relativistic invariance? The Schroedinger equation isn’t even Galilean invariant ( the mass comes through as a central charge, the probabilities are Galilean but not lorentz invariant)
The best reference for consistent histories is Bob Griffith’s excellent text (not to be confused with the other Griffiths)
Because I would expect a model that has a hope in hell of getting deeper toward the measurement problem than “shut up and calculate” to give a relativistically invariant account of the EPR, and because I expect such a model to be built on top of some form of QFT (as I mentioned in another reply, the number of particles is not conserved during the measurement, so the Hilbert space doesn’t cut it, you need something like a Fock space, second quantization etc.).
But the only way you are going to get relativistic invariance is to throw out the Schroedinger equation. The hope is that an interpretation makes it easier to move to QFT, NOT that a given interpretation will be Lorentz invariant (which is impossible, given the Schreodinger equation).
So far none of the interpretations of quantum are built on top of QFT, mostly because QFT isn’t yet formalized, its a hodge podge of heuristics that gets the right answer. The handful of axiomatic field theories don’t actually describe physical systems. Some people have a pipe dream that finding better quantum axioms will point the way toward better QFT axioms, but I’m not in that camp.
The SE should be a non-relativistic limit of whatever model is the next step. Not sure if it requires a formalization of QFT, it just needs to make decent predictions. Physicists are not overly picky. As long as it’s reasonably self-consistent. Or not even. As long as it helps you calculate something new and interesting unambiguously.
QFT IS the obvious next-step, but the reason people play with standard quantum formulations instead of trying to work in the context of QFT and ‘push the interpretation down’ is that QFT isn’t yet on firm footing.
::does some reading on Wikipedia::
Hmmm… apparently making QM play nice with Special Relativity isn’t quite as simple as using the Dirac equation instead of the Schrodinger equation, because the Dirac equation has negative energy solutions, and making it impossible for electrons to “decay” into these negative energy states requires kludges.
(Why is it that, the more I learn about QM, the more it seems like one kludge after another?)
Quantized wave function solves the negative energy problem, at the expense of introducing a bunch of infinities, some of which are easier to work around (renormalize) than others. For example, there is no way to usefully quantize gravitational field.
This isn’t quite true. What solves the problem isn’t quantizing wave functions, its insisting that positive energy propagate forward in time- i.e. picking the Feynman propagator (instead of the retarded or advanced propagator, etc) that solves the problem. You still have to make a division between the positive energy and negative energy pole in the propagator (unfortunately, all observers can’t agree on which states have positive and what states have negative energy, which is the basis of the Unruh effect- two observers accelerating relative two each other cannot agree on particle number).
Also, its a misconception that you can’t simply quantize the gravitational field. If you treat GR as an effective theory you can make calculations of arbitrary accuracy with a finite number of measured parameters, with just canonical quantization. The standard model is ALSO not a renormalizable field theory (not since the addition of neutrino masses). Weinberg has recently tried to make the argument that maybe GR + canonical quantization (i.e. gravity is asymptotically safe)
Thanks for the corrections, my area is mostly classical GR, not Standard Model physics. And a good point on the Unruh effect. As for quantizing GR, note the “useful” disclaimer. I am deeply suspicious of any technique that treats GR as an effective field theory on some background spacetime, as it throws away the whole reason why GR is unlike any other field theory. Weinberg is especially prone to to doing that, so, while I respect anything he does in HEP, I don’t put much stock into his GR-related efforts. If anything, I expect the progress to come from the entropic gravity crowd, with nothing to quantize.
When I worked in physics I did perturbative QCD stuff in graduate school and then effective theories for medium energy scattering, and finally axiomatic quantum field theories as a postdoc before I left physics for a field with actual employment opportunities (statistics/big data stuff).
But why shouldn’t GR be treated as just another field theory? It certainly has the structure of a field theory. Feynman and then Weinberg managed to show that GR is THE self-consistent, massless spin-2 field theory- so to that extent it IS just another field theory.
Treating GR as an effective theory works. I doubt that the theory is asymptotically safe, but for an effective theory, who cares? Why should we treat the matter part of the action any differently than we treat the spacetime piece of the action?
That’s a separate discussion, but let me just note that the action would have to be summed not just over all paths (in which spacetime?), but also over all possible (and maybe impossible) topologies, as well.